Representation of a three-dimensional (“3D”) object with a two-dimensional (“2D”) image is difficult is a non-trivial task. Holographic techniques have been used to create naked-eye stereovision images of 3D an object by recording the light wavefronts emitted from the object at a particular observation plane on a recording medium and the reconstructing the original light wavefronts by shining an appropriate light on the recorded medium, such that the light wavefronts appear to be emitted from the 3D object itself.
In modern optics theory, a complete description of light emitted from an object generally treats the wavefronts of light emitted from the object as complex wavefronts (i.e., having real and imaginary parts). An image of the object recorded on a recording medium, however, is generally represented by real functions of signal intensities. Therefore, the reconstruction of complex wavefronts from actual images that record only intensity data is non-trivial.
Conventional holography circumvents the problem of representing complex wavefronts with real signal intensity data by using an interference between signal and reference waves, through which the real component of complex wavefronts, Re[Ψ(r)], can be extracted, where Re[Ψ(r)] represents an addition of two conjugate waves, Ψ(r) as
      Re    ⁡          [              Ψ        ⁡                  (          r          )                    ]        =            1      2        ⁢                  (                              Ψ            ⁡                          (              r              )                                +                      Ψ            *                          (              r              )                                      )            .      Off-axis holography can extract a complex wavefront, Ψ(r), responsible for stereovision from Re[Ψ(r)] with the aid of a particular coherent illumination.
Other experiments using phase manipulation techniques can supplement the representation of the imaginary component of the wavefront, Im[Ψ(r)]. For example, the real and imaginary components of the wave function can be added in a computer image, Ψ(r)=Re[Ψ(r)]+iIm[Ψ(r)], but such techniques have not been extended to physical space.